However, when asked about the reported interest from the Catalans, he told a news conference on Wednesday: "I can not confirm it, I'm sorry".
The Catalan club ends its season after the Copa del Rey final against Alaves on Saturday.
Spanish media reports that Valverde should be named as successor to outgoing Barcelona coach Luis Enrique on Monday.
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"Right now I have no commitment to any team even though there are teams that have been interested in me", he said at a press conference to confirm his Bilbao departure.
"I haven't committed to any club, I haven't talked to anybody", Valverde said.
"I am very happy and thankful for the chance the club has taken on me", he told the club's website.
'He played here for Barcelona as a player and I think he could be a good option, as could others.
"I have had a lot of doubts, but my work here is done".
Now the situation is different and I have to consider whether I start a new project in another club.
"Ernesto Valverde will not continue as coach of the Athletic Club first team in the 2017-18 campaign", read a brief Athletic statement released on Tuesday. "Now I have to decide whether I will take on a new adventure, and it would have to be a challenging one".